MIMO Systems with Active Scatters and their Performance Evaluation

ABSTRACT

A communications system includes at least one receiver having receiving elements and a transmitter having transmitting elements to transmit signals to the receiving elements via wireless propagation channels. The transmitter includes a beam-forming network and a channel measurement unit. The beam-forming network receives input signal streams at its input ports and outputs one or more signals as shaped beams based on a set of composited transfer functions. The channel measurement unit performs measurements of components of channel status information to generate a set of point-to-point transfer functions and generates the composited transfer functions by computing linear combinations of the point-to-point transfer functions. Each of the point-to-point transfer functions characterizes propagation paths from one of the transmitting elements to one of the receiving elements. The composited transfer functions are point-to-multipoint transfer functions characterizing propagation paths from the input ports of the beam-forming network to one or more of the receiving elements.

RELATED APPLICATIONS

This application is a continuation of application Ser. No. 14/733,842,filed on Jun. 8, 2015, entitled “MIMO Systems with Active Scatters andtheir Performance Evaluation”, which is incorporated herein by referencein its entirety.

This application is related to

-   -   a. a U.S. patent application Ser. No.14/182,665, filed on Feb.        18, 2014, entitled “Multi-user MIMO via frequency re-use in        smart antenna,”    -   b. a U.S. patent application Ser. No. 14/193,540, filed on Feb.        28, 2014, entitled “Multi-user MIMO via active scattering        platforms,”    -   c. a U.S. patent application Ser. No. 14/288,707, “filed on May        28, 2014 Active scattering for bandwidth enhanced MIMO.”

All of the above are incorporated herein by reference in theirentireties.

DESCRIPTION

A multiple-user communications system for a point-to-multipoint(p-to-mp) via active scattering repeaters for efficient frequency reusedis described. The propagations channels dominated by multipath effectsare characterized by a composited transfer function technique. Onefeature of the systems is a multipath dominated MIMO communicationschannel comprising of multiple active scattering repeaters. Activescatters may be stationary, relocatable, or mobile and may beimplemented via man-made platforms such as on tops of trucks, unmannedauto mobiles, unmanned air vehicles (UAVs) in flight or parked UAVs.They may be implemented as small units in forms of light bulbs orextensions on lightbulb Socket. In addition to signal bandwidth,amplification levels, path delays on scattered or re-radiated signalsfor active scatters, positions and orientations of these scatteringdevices are individually controllable strategically to enhancemultiple-user MIMO communications systems. These are techniques todeploy controllable multipath propagation channels between a group oftransmitting terminals and another group of receiving terminals

BACKGROUND

Depicted in FIG. 1 is an idealized MIMO operation scenario with twopairs of user groups communicating between desired terminalsindependently and concurrently via a common frequency slot withoutmutual interferences. It would be nice to have total 3× frequency re-useof the allocated frequency slot; 2× for sending Sa and Sb from Atx toArx while 1× for transmitting Sc stream from Btx to Brx. In real world,techniques of MIMO are used to minimize mutual interferences by takingadvantages of multiple paths in the 3 communication channels.

The scenario may be expanded to more than two communicating groups,several of them might be communicating simultaneously. Distributed MIMOsystems usually addressed capacity in benign scenarios and are generallylimited to closed, narrowly focused systems, and do not address thecomplexity of radios automatically negotiating collaboration groups androles or the advanced signal processing to suppress interference andincrease energy to a particular location in order to maximize the linkcharacteristics. Further, existing work does not show how differentgroups can optimally communicate given this information.

SUMMARY OF THE INVENTION

This disclosure on communications systems is summarized as followed:

Communications channels from a transmitting source to multiple receivingdestinations are through active scattering from many distributedscattering devices including repeaters and transponders.

Frequency reuse is accomplished by directional diversity in transmittersvia formulations of point-to-multipoint (p-to-mp) composited transferfunctions and optimizations on the formulated functions under multiplespecified performance constraints for user identifications anddiscriminations.

Optimizations are through beam shaping techniques under performanceconstraints associated with locations indexed by user identifications orindexed by user element identifications.

A composited transfer function is optimized to represent an optimallyshaped beam, featuring a point-to-multipoint (p-to-mp) characteristicsincluding integrated multipath propagation effects of activelyscattering repeaters/transponders with favorable connectivity for onespecified user and discrimination against others.

A composited transfer function for transmitting data through multipathdominated channels. It is used for specified performance constraints fora shaped transmitting beam. A radiation pattern, or a wavefront, of theshaped beam is a linear combination, or a weighted sum, from radiationpatterns, or wavefronts, of multiple transmitting elements. The shapingof a radiation pattern are through altering the weighting parameters ofthe linear combination.

The shaping techniques may also be used for specified performanceconstraints for a shaped receiving beam. A reception pattern, or awavefront, of the shaped receiving beam is a linear combination, or aweighted sum, from reception patterns of multiple receiving elements.Shaping a reception pattern are through altering the weightingparameters of the linear combination, under performance constraints foroptimization via

-   -   1. Orthogonal beam (OB) criteria    -   2. Quiet zone criteria, and    -   3. Others.

Multiple concurrent beams are optimized under performance constraints bya set of many composited transfer functions. This disclosure describesexemplary embodiments on improving the operation and use of MIMOcommunication methods and systems for multiple users (MU) to re-use samespectrum such as through channel state information (CSI) to formperformance constraints in user-selection and/or rejection processing ontransmission or reception side. Embodiments pertain to wirelesscommunications through a multipath dominated channel, where themultipaths are dominated through man-made active scattering devicesincluding repeaters and transponders. These repeaters/transponders arein parallel scattering paths between a signal source to multipledestinations providing amplifications, delays and directionaladjustments for propagating signals.

When the sources and destinations are indoor for many embodiments,distributed repeaters serve as active scatters, which perform receiving,low-noise-amplifying, filtering, power-amplifying, and re-radiatingfunctions for signals through the repeaters. To avoid self-triggeredoscillations, many repeaters may feature slight frequency shifts, orstored and forward capability. Some repeaters may feature input andoutputs at a same carrier frequency but with large spacing betweentransmitting and receiving elements.

For many other embodiments, distributed transponders serve as activescatters, which perform functions of receiving, low-noise-amplifying,filtering, frequency translating, power-amplifying, and re-radiating forsignals in a transmitting frequency.

A repeater may consist of two transponders spatially separated in twolocations but cascaded functionally. A first transponder is forreceiving functions capturing desired signals in f1, which areamplified, filtered, and frequency translated before radiated out by aseparated aperture at f2m. A second transponder captures the amplifiedsignals at f2m, which are amplified, frequency translated, filtered, andpower amplified before radiated out by another separated aperture at f1.

In some embodiments, MIMO configurations feature a point-to-point(p-to-p) architecture with a source at a communication hub viaradiations to multiple repeaters and then re-radiations from theserepeaters to a destination which is in a common coverage of theserepeaters. The MIMO configurations may also feature apoint-to-multipoint (p-to-mp) architecture with a source at acommunication hub via radiations to multiple active scattering devices,and then re-radiation from the multiple scattering devices to multipledestinations.

In the MIMO systems of present invention, serving signals fortransmission to user equipment (UE) via multiple paths will utilizecomposited transfer functions selected and characterized based onchannel state information (CSI), which comprises of responses fromprobing signal sequences for a propagation channel dominated bymultipaths in accordance with a dynamic user distribution. Eachpropagating path may feature unique functional effects from a set ofscattering devices. The composited transfer functions are constructed orshaped to be “user dependent” with enhanced responses to a selected userand suppressed ones for other users. When operating in coordinatedmodes, more cooperating UEs are configured to suppress interference toother UE using the same frequency resources. Optimization methods forthe composited transfer functions based on selected criteria have beenpresented in related patent applications listed above. Some embodimentsrelate to coordinated point-to-multipoint (p-to-mp) communications inspoke-and-hub configurations. The criteria for shaping the compositedtransfer functions for a transmitter in a communications hub may includethose in many beam-shaping techniques, such as orthogonal beams (OB),quiet-zones, and others. Some embodiments relate to wavefrontmultiplexing (WF muxing)/demultiplexing (demuxing) as means forcoordinated or organized concurrent propagations through multipathdominated channels. As a result, methods for calibrations andequalizations among multiple path propagations become possible. Some arethrough forward paths only. Consequently, implementations of techniqueson coherent power combining in receivers for enhanced signal-to-noiseratios (SNR) are simple and cost effective.

In short, there are two features in the disclosures for multi-user MIMOsto achieve frequency reusing for over hundred folds deterministically,not just statistically;

-   -   1. Composited Transfer Functions        -   Featuring point-to-multipoint (p2mp) performance,        -   generated by            -   linear combinations of multiple                Channel-Status-Information (CSI) components as P/Q                matrixes,            -   Specified performance constraints,            -   P/Q matrix optimized via Beam Shaping Optimization                programs.    -   2. Multipath via active scattering;        -   Scattering by active electronic devices on movable or            re-locatable platforms;        -   enabling some controls over multipath propagation channels,        -   Simple techniques to have >>10× frequency reuse potentials

Presented are MIMO communications architectures among terminals withenhanced capability of frequency reuse by strategically placing activescattering platforms at right places. These architectures will notdepend on multipaths passively from geometry of propagation channels andrelative positions of transmitters and those of receivers. For advancedcommunications which demand high utility efficiency of frequencyspectrum, multipath effects are purposely deployed through inexpensiveactive scattering objects between transmitters and receivers enable asame frequency slot be utilized many folds such as 10×, 100× or evenmore. These active scatters are to generate favorable geometries ofmultiple paths for frequency reuse through MIMO techniques. Thesescatters may be man-made active repeaters, which can be implemented assmall as 5 to 10-watt lightbulbs for indoor mobile communications suchas in large indoor shopping malls. The architecting concept can becertainly implemented via mini-UAV platforms parking on tops oflight-poles, or tree tops, or tops of stadiums, or circulating in small“figure-8” or small circles slowly. This system can be pushed tofacilitate >>100× frequency reuses among users. It may be one ofpossible solutions for 5G deployment and many other applications whichneeds high efficiency in frequency utility.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an idealized MIMO operational scenario for 3× frequencyreuse over a common frequency slot; 2× for between [Atx, Arx] and 1× forbetween [Btx, Brx].

FIG. 2 depicts a flow chart of simulating CSI for MIMO and generating Txor Rx CTF's based on obtained CSI via performance optimization in Tx orRx sites, respectively.

FIG. 3 depicts geometrical distributions for calculating CSI and CTF;including transmitting and receiving antenna elements and scatters.There are two communications pairs [Atx, Arx] and [Btx, Brx] utilizing asame frequency slot. Each of [Atx, Arx] features 3 antenna elements, andeach of [Btx, Brx] features 2 antenna elements.

FIG. 3A depicts simplified architecture of an active scattering devicevia two cascaded transponders; a first transponders with input at f1 andoutput at f2 while a second transponder are in series with the first onefeatures an input at f2 and an output at f1. F1 and f2 may be in S-bandand Ku band, respectively. These two transponders, one for S-to-Ku bandand the other for Ku-to-S band, reasonably separated to minimizeself-oscillations, are configured to form a S-band repeater.

FIG. 3B depicts coordinates of key elements in a simple geometry: with10 representative active scatters (I) and two communications pairs [Atx,Arx] and [Btx, Brx] utilizing a same frequency slot each with multipleantenna elements. In all transmitters and receivers here, each featuresthree antenna elements.

FIG. 3C depicts coordinates of key elements in a simple geometry: with 5representative active scatters (s3, s4, s5, s6, and s7) (II), twocommunications pairs [Atx, Arx] and [Btx, Brx] utilizing a samefrequency slot. Each of [Atx, Arx] features 3 antenna elements and eachof [Btx, Brx] features 2 antenna elements. The positions of all antennaelements and those of the 5 active scatters are indicated.

FIG. 3D depicts coordinates of key elements in a simple geometry: with 5representative active scatters (s3, s4, s5, s6, and s7) (III). Thepositions of all antenna elements and those of the 5 active scatters areindicated. Path loss and phase delay calculating formulations arehigh-lighted from element “a” of a first transmitter Atx to one of the 5scatters, s3.

FIG. 3E depicts functional block diagram of calculating capturedradiation power in a receiver from a transmitter with omni-directionalor isotropic transmission following a link equation.

FIG. 3F depicts functional block diagram of calculating capturedradiation power in a receiver from a transmitter with directionaltransmission following a link equation.

FIG. 4 depicts channel transfer functions (CTF) in H-matrices; with 6 Txelements (a, b, c, d, e, f) and 5 Rx elements (1, 2, 3, 4, 5). A first Hmatrix characterizes from elements of a first transmitter Atx to allelements in two receivers Arx and Brx. A second H matrix characterizesfrom elements of a second transmitter Btx to all elements in the tworeceivers Arx and Brx.

FIG. 5 depicts calculated channel status information (CSI) between 3 Txand 5 Rx elements based on 5 active scatters and LOS propagation paths;two important components; path loss and phase delays.

FIG. 6 depicts a set of Tx CTFs for a 1st transmitter Atx; 3 shapedbeams generated by a Tx beam-forming-network (BFN).

FIG. 7 depicts 3 Tx CTFs, respectively associated with 3 individuallyshaped concurrent beams.

FIG. 8 depicts 3 Tx CTFs associated with 3 individually shapedconcurrent beams in P-matrix optimization in the 1st transmitter Atx.

FIG. 9 depicts an optimized radiation pattern to peak at element #1 fromthe first transmitter via LOS paths only. The inherent geometry of thetransmitting array feature a resolution separating a peak at element #1and a null near the directions of elements #4 and that of #5; but notadequate for differentiating radiations at element #2 and #3 adjacent tothe peak direction at element #1.

FIG. 10 depicts optimized radiation patterns from the first transmitterwith both LOS effects and those from multipaths due to the 5 scattersunder three different sets of performance constraints pointed atelements #1, #2, and #3, respectively.

FIG. 11 depicts a simplified functional block diagram for Tx elements ofa user shared among cooperative transmitters of other users; Atx of userA using two Btx's elements from user B.

FIG. 12 depicts 3 optimized CTFs assuming LOS effects only, eachpointing toward one Rx element while steering two nulls to the other twoRx elements of the Arx receiver, and forming additional two nulls to Rxelements 4 and 5 of the Brx receiver

FIG. 13 depicts two optimized radiations; all 5 elements in Atx and Btxare used in optimizing a CTF pointing toward Rx element 2 while steering4 nulls to Rx elements 1, 3, 4 and 5; panel (A) assuming with loseffects only and panel (B) with effects from both los and scatters.

FIG. 14 depicts two optimized radiations over a 100m distance; panel (A)with LOS effects only and panel (B) with effects from both LOS andscatters over a Dy along y-axis; where Δy=10 m. Calculations are viaMatlab simulations

FIG. 15 depicts 3 CTF patterns for optimized beams pointing to Rxelement 1 of Arx with scatters distributed in Δy; Panel A with Δy at 20m, Panels B and C Δy at 40 m, and 80 m, respectively. Calculations arevia Matlab simulations

FIG. 16 depicts a relationship (including a geometry) of calculating areceived power at a destination, Y, from a power source, X, throughcalculation of scattered power by a virtual scatter, Z, in between vscalculating power at the same destination directly via a Line of Sight(LOS) Propagation; a Fetch factor (Ff) is introduced in the virtualscatter technique to make the power arriving at destination identical tothe direct diffusion result from a LOS propagation path.

FIG. 16A depicts formulations in calculating a Fetch factor (Ff); powerat a destination via line-of-sights path, and power at destination via avirtual scattering mechanism.

FIG. 16B depicts formulations in calculating a Fetch factor (Ff) for avirtual scatter so that the resulting power in a destination from a LOSmethod shall be identical to that via calculating scattering effects bya virtual scatter

FIG. 16C depicts calculated distributions of A Fetch factor (Ff) in dBdue to Propagation effects.

DETAILED DESCRIPTION

FIG. 1 depicts an idealized MIMO operation scenario with two pairs ofuser groups communicating between desired terminals independently andconcurrently via a common frequency slot without mutual interferences.The first group is between a first transmitter Atx 122 with 3transmitting (Tx) elements and a first receiver Arx 124 with 3 receiving(Rx) elements. It would be nice to have total 3x frequency re-use of theallocated frequency slot; 2× for sending Sa via a first channel 134 andSb via a second channel 136 from Atx to Arx and while 1× fortransmitting Sc stream via a third channel 132 from Btx to Brx. In realworld, techniques of MIMO are used to minimize mutual interferences bytaking advantages of multiple paths in the 3 communication channelsconcurrently utilizing a common frequency slot. The scenario may beexpanded to more than two communicating groups, several of them might becommunicating simultaneously.

Our proposed advanced MIMO solutions for enhanced bandwidth utility arebased on a patented method a U.S. patent application Ser. No.14/182,665,filed on Feb. 18, 2014, entitled “Multi-user MIMO via frequency re-usein smart antenna” in generating Composited Transfer Functions (CTF)based on measured channel status information (CSI) of conventional MIMO.Proposed solutions using active scatters for MIMO communications amongmultiple user groups will quantify the amount of interferencesuppression (both in terms of interference power levels and number ofdistinct interferers) possible in addition to the inter-groupcommunication bandwidth, as well as optimization techniques for usingsome or all group members for a single communications link, or multiplecommunications links.

A flowchart of methods simulating or obtaining CSI information via realtime measurements and generating CTF's are depicted in FIG. 2. There arethree steps. The first step 0210 will utilize conventional CSIinformation collected from “multiple point-to-point (p2p) paths”initiating from a transmitting (Tx) element to a receiving (Rx) element0212 including via a scatter and then to the Rx element for allscatters, as well as via a line-of-sight (LOS) direct path to the Rxelement individually. This simulation step requires knowledge ofpositions and orientations of Tx and Rx elements 0201 and locations forall active scatters 0204.

The second step 0220 is to group all parallel paths from a Tx element toa Rx element as a p2p transfer functions. The connectivity performancescannot be specified in directions in most MIMO antenna geometries butthrough position indexing techniques on both transmit and receivingelements involved.

The third step 0230 will involve optimally weighting and summing ofmultiple p2p functions to become composited transfer functions (CTF)which must meet various performance constraints 0206. Optimizations 0230may be realized through optimization algorithms 0208 which may includeiterative techniques. The connectivity performance optimization alsocannot be specified in directions in any MIMO geometries but throughposition indexing techniques on both transmit and receiving elementsinvolved. The results may be grouped into two categories; (1) a firstgroup of P-2-MP Tx CTF 0232 characterizing a Tx port to selected Rxelements and (2) a second group of MP-2-P Rx CTF 0234 featuring a Rxport from selected Tx elements.

In this disclosure we shall focus on how a function in the first group,P-2-MP Tx CTF 0232, is created and its connectivity and discriminationperformances are evaluated over a coverage area of our interest. Thesame principles can be extended to examples of the second group, MP-2-PRx CTF 0234.

CSI Calculation in the Simulation

FIG. 3 shows geometrical distributions in X-Y plane for 2 transmitters0710 and 0410, 2 receivers 0722 and 0732, and 5 scatters 0310 infollowing simulated results. The coordinates for all 5 transmitting, 5receiving elements and 5 scatters are indicated in meters. A piece ofCSI comprises a set of propagation information between a transmittingelement and a receiving element featuring a point-to-point (p2p orp-2-p) transfer function. As depicted a CSI through a multipathdominated channel between a transmitting (Tx) element “a” of three Txelements 0716 of an Atx transmitter 0710 to a receiving element “4” oftwo Rx elements 0724 of a Brx receiver 0722 is represented as h_(4a) (anelement in a H matrix) representing a path attenuation and a phase delayaggregated from multipaths through the communication channel fromelement “a” of the 3 Tx elements 0716 to element “4” of the 2 Rxelements 0724.

In calculations of all following examples, it is important to note thatthe receiving elements are indexed along a line parallel to the y-axisat x=x0. In most of the examples, xo is set at 10 m. The element indexesare set to show any adjacent receiving elements are separated by a deltanumber of indexes more than 1. As a result, elements can be identifiedvia element indexes and the element positions along the line of x=10 mparallel to the y-axis. Therefore, CTF performance certainly can beplotted as function of y position alone the line at x=10 m and also maybe plotted or interpreted as a function of indexes for receivingelements. With such a convention, antenna engineers may associate theirknowledge on antenna directional patterns to the plots of CTFs. We willcome back to FIG. 3 and discuss more on simulation assumptions.

FIG. 3A illustrates an example of a repeater 0310 to function as anactive scatter. It comprises of two cascaded transponders 0312 and 0314,each with amplifications and frequency translation functions. It isarranged with a finite short distance or orientations to minimizepotentials of self-oscillations which is a degrading feature aconventional repeater usually exhibit due to its outputs unintentionallycoupling back to its inputs when operating in a high gain mode. Thefirst transponder 0312 features an input at f1 and output at f2, whilethe second transponder 0314 has an input at f2 and an output at f1. Theexample in FIG. 3 depicts an S-band communication channel between a Txelement 0392 and a receiving element 0398 separated at >20 meters. AnS-band repeater 0310, located in between the Tx element 0392 and the Rxelement 0398, comprising of two transponders separated about 1 meterapart and interconnected in Ku band, deliver a range of aboutamplifications from 50 to 70 dB typically in various configurations.

In our current Matlab simulation configurations as depicted in FIG. 3B,flexibility is limited for a given study. However, it is still possibleto use up-to 10 active scatters in calculations among communications oftwo pairs of users [Atx 0710, Arx 0732] and [Btx 0410, Brx 0722] andwith a maximum of total 6 Tx elements 0716 and 0416, and total 6receiving elements 0724 and 0734. Simulation configurations can be“degenerated” to, for instance, a scenario with one transmitterfeaturing 6 Tx elements and two separated receivers; one with a group of2 Rx elements and the other with another group of 3 Rx elements.

In this disclosure, most of the simulation results are from a geometrydepicted in FIG. 3C; with 5 active scatter 0310 in calculations amongcommunications of two pairs of users [Atx 0710, Arx 0732] and [Btx 0410,Brx 0722] and with 5 transmitting elements 0716 and 0416 total, and 5receiving elements 0724 and 0734 total. The 3 elements 0716 for Atxtransmitter 0710 are in a linear array with a 10 cm spacing betweenadjacent elements. The 2 elements 0416 for Btx transmitter 0410 are alsoin a linear array with a 10 cm spacing between adjacent elements. Thetwo transmitters are separated by 5 meters in y-direction. AS shown, theAtx transmitter 0710 and the Arx receiver 0732 are separated by 25meters in x-direction. On the other hand, the Btx transmitter 0410 andthe Brx receiver 0722 are separated by 25 meters in x-direction and 10meter in y direction. The 5 active scatters are −15 meter away from thetwo transmitters and 10 meters away from two receivers in x direction,and are distributed in y direction almost linearly with spacing of 2 or3 meters between adjacent ones.

Transmitting elements 0716 for Atx 0710 in a (x, y, z) coordinate are at(−15, 0.1, 1.6), (−15, 0.0, 1.6), and (−15, −0.1, 1.6). The receivingelements 0734 for Arx 0732 in the (x, y, z) coordinate are at (10, 0.1,1.6), (10, 0.0, 1.6), and (10, −0.1, 1.6), respectively.

Transmitting elements 0416 for Btx 0410 in the (x, y, z) coordinate areat (−15, −5.0, 1.6), and (−15, −5.1, 1.6). The receiving elements 0724for Brx 0722 in the (x, y, z) coordinate are at (10, 5.1, 1.6), and (10,5.0, 1.6), respectively.

The 5 active scatters 0310 in the (x, y, z) coordinate are at (−1.0,5.0, 3.0), (1.0, 3.0, 3.0), (0.0, 0.0, 3.0), (−1.0, 2.0, 3.0), and (1.0,−5.0, 3.0), respectively.

It is intended for S-band operations at 2.5 GHz with a wavelength of 12cm. The gain in active scatters are set at 50 dB as a fetch factor. Seedetails in FIG. 16.

FIG. 3D depicts path loss and phase delay calculation. Calculatingformulations are high-lighted from element “a” of the three elements0716 of a first transmitter Atx 0710 to one, “s3”, of the 5 scatters0310. Coordinates of 5 representative active scatters (s3, s4, s5, s6,and s7) 0310 are shown. Indicated also are the positions of all antennaelements; including three 0716 from Atx 0710, two elements 0416 from Btx0410, three 0734 from Arx 0732, and two elements 0734 from Brx 0732.Formulation of received electric field by the scatter “a”, Ea23,following convention link calculations, is repeated as following;

Ea23=sqrt[Pa2*Gt/(4π*Ra23²)*Areff]*exp(jkRa23)   (1)

where;

-   -   Pa2: radiated total power by element “a”;    -   Gt: antenna gain of element “a”;    -   Ra23: distance from element “a” to scatter “s3”;    -   Areff=λ²*Gr/4π;    -   Gr: receiving antenna gain of “s3”;    -   k: wave number and k=λ/2π.

FIG. 3E depicts functional block diagram of calculating capturedradiation power in a receiver 0330 from a transmitter 0310 withomni-directional or isotropic transmission following a link equation.Divergent power density from the transmitting source 0310 at variousdistances 320 are calculated. Using similar link equation like equation(1), captured power by a receiving antenna element 0330 is alsocalculated.

FIG. 3F depicts functional block diagram of calculating capturedradiation power in a receiver from a transmitter with directionaltransmission following a link equation. Divergent power density from thetransmitting source 0310 at various distances 320 are calculated. Usingsimilar link equation like equation (1), captured power by a receivingantenna element 0330 is also calculated.

The H matrix in FIG. 4, currently depicted as two 3×6 submatrixes,features a 6×6 matrix 0714 representing 36 individual transfer functionsfor 6 transmitting elements and 6 receiving elements. 5 of the 6elements in both Tx and Rx are distributed in two groups ofcommunications pairs; [Atx 0710, Arx 0732], and [Btx 0410, Arx 0722].The C group [Ctx 0420, Crx 0430] features one Tx element (element “f”)0426 in Ctx 0420 and one Rx element (element 6) 0436 in Crx 0430. It maybe added in different operation scenarios demonstrating different degreeof freedoms and spatial resolutions.

The effects of the 6^(th) elements in the H matrix are additionalcomponents in the 6^(th) row and those in the 6^(th) columns in a bluecolor. In fact, without the third pairs, the H matrix 0714 features twosub-matrixes. The first is a 5×3 sub-matrix for the transfer functionsfrom the 3 Tx elements 0716 of Atx 0710 to all 5 receiving elements 0724and 0734. The second is a 5×2 sub-matrix for the components from the 2Tx elements 0416 of Btx 0410 to all 5 receiving elements 0724 and 0734.

FIG. 5 depicts an example with 15 calculated transfer functionscomponents in a first 3×5 H submatrix for the 3 Tx of elements (a, b,and c) 0716 of the Atx 0710 to 5 Rx elements (1, 2, 3, 4, and 5) 0724and 0734 in FIG. 3.

Formulations of Tx Composited Transfer Functions (Tx CTFs)

A transmit CTF comprises a beam forming network 0712 for a dynamicshaped beam followed by an H matrix 0714 with many p2p transfer functioncomponents as shown in FIG. 6. We have added feedback paths forobtaining or measuring CSI 0708 in FIG. 7. Examples of performanceconstraints 0704 are delineated.

In our simulation geometries in FIG. 3, the component, h4a, represents atransfer function with effects of 6 parallel paths from the Tx element“a” of the 3 array elements 0716 to the Rx element “4” of the two arrayelements 0724. The 6 paths comprise of a line-of-sight (LOS) path, and 5parallel paths due to scattered by 5 separated scattering centers (s3,s4, s5, s6, and s7) 0310 individually. Path attenuations and phasedelays from every scattering path are calculated from two propagationsegments in series; as an example, from a Tx element (element a) of the3 array elements 0716 to a scatter (s6) in 0310 and then from thescatter (s6) in 0310 to an Rx element (element 4) of the 2 arrayelements 0724. We may even consider that Atx 0710 and Btx 0410 are on afirst moving platform and Arx 0732 and Brx 0722 are on a secondplatform.

As depicted in FIG. 6, an input of a transmit CTF, say Ax, is assignedto a beam-forming-network (BFN) 0712 input of the Atx, while the CTFoutputs may be specified as power received at all receiving elements ofmany receivers; such as two array elements 0724 of Brx 0722 and threearray elements 0734 of Arx 0732. A Tx CTF in this case features aP-to-MP function with a BFN-A 0712 followed by [H_(A)] propagationmatrix 0714. The coupling or interconnects between the BFN-A 0712 andthe CSI in [H_(A)] 0714 are through the 3 transmitting antenna elements0716.

The selected CSI measurements in the H matrix, [H_(A)] 0714, for the TxCTF are initiated from 3 Tx elements 0716 of the transmitter Atx 0710and “ended” at 5 receiving elements 0724 and 0734 of both receivers, Arx0732 and Brx 0722. One of the 3 Tx CTF in FIG. 6 shall enable atransmitting signal string, Ax, to reach all 5 Rx elements on thereceiving terminals with specified performance constraints byreplicating the input Ax into three parallel streams in BFN-A 0712followed by a optimized amplitude and phase weighting processing, beforeconnected to the three Tx elements 0716. Thus an optimally weighted Axsignal stream is then launched, by the three Tx elements 0716, intomulti-path dominated propagation channels characterized by the [H_(A)]matrix 0714.

Outputs of the [H_(A)] matrix 0714, also the outputs of the Tx CTF, atthe 5 Rx elements may be assigned to inputs of a receiver DSP forfurther processing. On the other hand, the same outputs may be specifiedas desired performance constraints for optimization processing. Thereare three inputs, Ax, Ay, and Az, to the BFN-A 0712, which shall beassociated with different sets of performance constraints such as onpower density on various receiving elements; elements 1 through 5. Afirst stream of data, Ax, will be radiated by all 3 transmittingelements (element “a” through element “c”) 0716 with a unique weightingdistribution on radiated Ax by the 3 elements 0716. Concurrently, asecond and a third data streams, Ay and Az, will also be transmitted bythe same three elements 0716 accordingly.

The inputs and the outputs of the BFN-A 0712 are characterized in thematrix equation depicted on the lower left corner of FIG. 6. The 3-to-3BFN (BFN A) 0712 functions represented by a P matrix with 9 weightingparameters are optimized under 3 sets of performance constraints asindicated in FIG. 7 and FIG. 8.

All three beams optimized by the BFN-A 0712 will generate radiationpatterns, after the multipath channel propagation, resulting 3 sets ofindividual transmitted or radiated wavefronts in which each shall favorone of the Rx elements 0734 of a first receiver Arx 0732 anddiscriminating against all Rx elements 0724 of a second receiver Brx0722.

Formulations of Rx Composited Transfer Functions (Rx CTFs)

A receiving (Rx) CTF is a weighted sum of multiple p2p CSI and shallfeature a prescribed characteristic of multiple inputs in a group oftransmitters and a receiving output in a receiver; specifying desiredperformance constraints at various transmitting elements such as 0716 ortransmitters such as 0710. Current measurements on the selected CSI foran Rx CTF are initiated from many Tx elements such as 0716 of varioustransmitters such as 0710 and “ended” at various receiving elements of areceiver, such as the receiver Arx 0732 to enable received signals bythese Rx elements 0734 connected to a processing in the receiver Arx0732 for optimized amplitude and phase weighting before summing. Thecombination of the selected CSI and the optimized receiving processor iscalled a Rx CTF. Output of the Rx CTF may be assigned to a DSP input ofthe receiver, while the CTF inputs at various Tx elements such as 0716may be specified as desired performance constraints.

We will not do more on Rx CTF formulations and optimizations in thisdisclosure.

Unique Features in the CTFs Design Concepts

Composited Transfer Functions (CTF)

-   -   Tx CTF featuring point-to-multipoint (p2mp) performance as shown        in FIG. 8,    -   Rx CTF featuring multipoint-to-point (mp2p) performance,    -   generated by linear combinations of multiple        Channel-Status-Information (CSI) components as P matrixes 0712        for Atx 0710 and/or Q matrixes for Btx 0410;        -   with specified performance constraints P/Q matrix optimized            via Beam shaping optimization programs 0706.        -   Optimization via collaborated element indices not physical            locations or angles.

Multipath via active scattering.

-   -   Scattering by active electronic devices on movable or        re-locatable platforms;    -   enabling some controls over multipath propagation channels.    -   Simple techniques to have >>10× frequency reuse potentials

Intragroup networks among multiple users in a group will feature similarconcepts of ground-based beamforming (GBBF) for existing mobilesatellite communications or remote beam forming networks (RBFN) for DBSsatellites.

Simulation Results for Two Groups of Communication Pairs for N Times ofFrequency Reuse

Current simulations are setup according to a geometry depicted in FIG. 3for scenarios under the following conditions;

-   -   1. all Tx elements are aligned along a line parallel to y-axis        at x=Xt where Xt is a constant ranging from −100 m to −5 m    -   2. all Rx elements along a line parallel to y-axis at x=Xr where        Xr is a constant ranging from 10 m to 100 m    -   3. all scatters are distributed near a line parallel to y-axis        at x=Xs where Xs varies between −1 m to 1 m. They are placed in        a range of ΔY near x=Xs. Scatter centers between −100 to 100 m        with ΔY ranges from 0 to 200 m.

As a result, Tx radiation patterns are calculated over regions ofinterest and resulting pattern cuts are “plotted” along lines parallelto the y-axis at x=Xr and nearby. Similarly, Rx patterns are calculatedover regions of interest and resulting pattern cuts are “plotted” alonglines parallel to the y-axis at x=Xt and nearby.

All simulations are run assuming signals at 2.5 GHz. Optimization is viaperformance constraints specified by Rx element position indices onlynor through element coordinates. However, the performances in terms ofradiation patterns are all plotted along line length index.

The simulated results in here are all from Matlab based CVX. SDS doeshave its own optimization algorithms with more flexibility and lessstringent on setting up performance constraints which may not beformulated on convex surfaces.

Tx Groups and Rx Groups in S-Band are Separated by 25 Meters

The following simulation results will show, among other phenomena,multipath effects from light of sight (LOS) propagations with andwithout the effects of scatters to the optimization capability in CTFs.Current simulations are setup for scenarios under the followingconditions;

-   -   1. all Tx elements are lined up at x=Xt where Xt is set at −15        m,    -   2. all receiving elements parallel to y-axis at x=Xr where Xr is        at 10 m,    -   3. all scatters are distributed near a line at x=Xs where Xs may        vary between −1 m to 1 m. They are also placed in a range of ΔY        near x=Xs, where ΔY is set at 20 m.

Independent Transmitters without Cooperation via Feeder Links

CTFs or radiation patterns in FIG. 9 and FIG. 10 are results of beamforming on elements from a single transmitter but with performanceconstraints on elements from multiple receivers.

FIG. 9 depicts one of the optimized radiation patterns 0914 from 3elements (a, b, and c) 0716 in the first transmitter Atx 0710 vialine-of-sight (LOS) paths only without effects due to scatters. Theshaped transmitting radiation pattern 0914 is a 2-D plot with a verticalaxis in dB representing propagation gain and a horizontal axis forpositional or directional indexes for receiving elements. It is designedto have a desired reference radiation level (usually a high gain level)to one of antenna elements (element 1) 0734 of the desire receiver Arx0732 and concurrently steering nulls toward elements (elements 4 and 5)0724 of the second receiver of Brx 0722.

The received array elements are indexed according to their locationsalong the line parallel to the y-axis at x=10 m. As a result of theircoordinates in y-direction, elements #1, #2 and #3 of the receivingarray 0734 for the first receiver Arx 0732 are indexed as 169, 165 and161 while element # 4 and #5 of the receiving array 0724 of the secondreceiver Brx 0722 are marked as 369 and 365.

The Tx radiation pattern 0914 by the three elements a, b, and c of thefirst transmitting array 0716 is optimized for Ax transmission and isshaped by a first set of performance constraints using an optimizationalgorithms; (1) a fixed power density (a specified reference) at Rxelement 1 of the first receiving array 0734 and (2) average powerdensity level at Rx elements 4 and 5 of the second receiving array 0724is less than −30 db below the reference which is set at 0 dB in thisexample, and (3) radiated power in a receiving coverage area withposition indexes ranged from 0 to 500 is minimized. Vertical auxiliarylines are drawn to facilitate viewing corresponding pattern levels amongmultiple receiving elements.

There are two more nearly identical shaped patterns (not shown) for Ayand Az transmissions. Their calculations are based on a different firstperformance constraint from the above mentioned 3 performanceconstraints; to have a fixed high-power density at element 2 for Aypattern, and to have a fixed high-power density at element 3 for Azpattern, respectively. The other two constraints are identical.

It is clear that the first transmitter 0710 with the Tx array elements0716 distributed over a 20 cm linear aperture or 1.67 wavelength,without effects of scatting of active scatters 0310, features spatialresolutions (with a 3 dB beamwidth about 35° near its boresight) notadequate for separating responses of Rx elements 1, 2, and 3 of the 3 Rxarray elements 0734 of the first receiver Arx 0732. A rule of thumb maybe stated that a spatial resolution of an aperture is about ½ of its 3dB beamwidth. These Rx elements 0734 are >25 m away from the Tx arrayelements 0716 and are spaced by 0.1 m among their own adjacent elements0734. However, the transmitter spatial resolutions appear barelyadequate to separate elements of the Rx array 0734 of Arx 0732 fromthose 0724 of Brx 0722. These two receivers are 5 m apart and ˜25 m fromthe radiating aperture 0716 of Atx 0710.

The best achievable frequency re-use is 2×; 1× between Atx 0710 and Arx0732 as shown in FIG. 10; and another 1× between Btx 0410 and Brx 0722even with post-processing in both receivers 0722 and 0732.

FIG. 10 depicts three optimized radiation patterns 1012, 1014 and 1016from the same 3 elements (a, b, and c) of the transmitting array 0716 inthe first transmitter Atx 0710 with both effects from scatters 0310 andthose from line-of-sight paths. Shaped radiation patterns respectivelyoptimized for Ax, Ay and Az are designed under the identical set ofperformance constraints as those in FIG. 9. It is clear that the firsttransmitter 0710 with multipaths due to scattering from active scatters0310 features “better” spatial resolutions adequate to separate the Rxarray elements 0734 of Arx 0732 from those 0724 of Brx 0722, and notquite for separating effects among the elements 1, 2, and 3 of the3-element Rx array 0734 of Arx 0732.

It may require additional processing in Arx 0732 to separated threeindependent data streams Ax, Ay, and Az by linear processing of receivedsignal streams by the three receiving elements 1, 2, and 3 of the3-element Rx array 0734. The best achievable frequency re-use for thisconfiguration is 4×; in which 3× between Atx 0710 and Arx 0732 (withadditional processing on receiver Arx 0732); and ony 1× between Btx 0410and Brx 0722 even with post-processing capability in receiver Brx 0722.

Cooperative Transmitters Via Feeder Links

FIG. 11 depicts a signal flow block diagram for a 1^(st) transmitter Atx0710 with its 3 own Tx elements 0716 while utilizing additional 2 Txelements 0416 on a 2^(nd) transmitter Btx 0410 for optimizing three CTFsbelongs to the first transmitter Atx 0710. The intra-networks 1120 asshown between Atx 0710 and the BFN-B 1134 of the Btx 0410 are alsoreferred to as feeder links or background networks. We will be usingremote beam forming (or ground based beam forming) techniques which havebeen implemented in many existing mobile satellite communicationssystems. The new P-matrix 0712 associated with the 3 CTFs features a 3×5matrix, where the 15 parameters are dynamically optimized. Dynamiccalibrations and equalizations (not shown in here) among paths between aTx beam forming processor and various remote Tx elements 0416 will beimplemented via patented wavefront multiplexing techniques which wereproposed for DBS satellite broadcasting.

CTFs or radiation patterns in FIG. 12 through FIG. 15 are results ofbeam-forming-networks (BFN) on elements from a single transmitter (suchas Atx 0710) and on elements from other transmitters (such as Btx 0410)via remote-beam forming mechanisms. The element weighting parameters orweights in the BFNs are optimized under performance constraints onelements from multiple receivers (such as Arx 0732 and Brx 0722) atdestinations.

FIG. 12 depicts three radiation pattern-cuts 1202, 1204, 1206 from all 5transmitting elements coherently combined with optimized weightingsassuming LOS effects only. They are 2-D plots; each with a vertical axisin dB representing propagation gain and a horizontal axis in positionalor directional indexes for receiving elements, the same presentationformat as that in FIG. 9. It is designed to have a desired referenceradiation level (usually a high gain level) to one of Rx antennaelements (element 1) 0734 of the desire receiver Arx 0732 andconcurrently steering nulls toward elements (elements 4 and 5) 0724 ofthe second receiver of Brx 0722. The 3 elements in Atx 0710 and 2elements in Btx 0410 are all used in optimizing the independent 3 CTFs.Panel A 1202 features a reference direction pointing toward Rx element 1of the 3-element Rx array 0734 while steering two nulls to the other tworespective Rx elements (element 2 and 3) of the 3-element Rx array 0734of the Arx receiver 0732, and forming additional two nulls to Rxelements 4 and 5 of the 2-element Rx array 0724 of the Brx receiver0722.

Similarly, panels B 1204 and C 1206 feature, individually, a referencedirection pointing toward Rx elements 2 and 3 of the 3-element Rx array0734, respectively. The corresponding beam weight vectors (BWV) areshown on the lower left corners of the respective panels, each featuring5 complex parameters representing the optimized weighting for thetransmitting elements 0716 and 0416. The optimal beam shaping is aimingfor 5× frequency re-use via orthogonal beams (OB). These three are OBradiation patterns, which feature 3 sets of BWVs corresponding to 3 OBradiation patterns. Any one beam peak of the 3 OB radiations is alwaysat nulls of all other 2 OB radiations. It is clearly noticed that thereare no significant different radiated power levels (with respect to amaximum or an averaged power density level over the plotted range) inthe three panels at the intended beam peaks (the desired beam positionsat element 1, 2, and 3 of the 3-element Rx array 0734 of Arx 0732). Thepeak and the averaged radiation levels, respectively, in all threepanels feature ˜35 dB and ˜25 dB above the reference at 0 dB in variousdirectional indexes. Rx element 1, 2, 3 of the 3-element Rx array 0734are at the position index 169, 165 and 161 respectively.

There are total 5 possible Tx OB radiation patterns from 5 antennaelements. We only show 3 of 5 OB radiation patterns, which are fortransmitting a signal stream A(t) through Atx 0710. As shown in FIG. 11,the signal stream A(t) is segmented by a series-to-parallel (S2P)converter 0702 into three segmented streams; Ax, Ay, and Az, which arethree inputs to the CTFs 0712. The three CTFs shall take advantage of 3local elements 0716 in Atx 0710 and 2 remote elements 0416 in Btx 0410.

The other two OB radiation patterns (not shown but in forms of two CTFs)are for transmitting signals of B(t) via 2 local elements 0416 in Btx0410 and 3 remote elements 0716 in Atx 0710. B(t) is also segmented intotwo segments of Bx and By by a second S2P 1132 before transmissions.There shall be no mutual interferences among beams featuring a set of OBradiation patterns at intended destinations.

FIG. 13 depicts two Tx patterns from coherent radiations by 5 elements;3 Atx elements 0716 and 2 Btx elements 0416; panel A 1302 assuming withLOS effects only and panel B 1304 with effects from both LOS andscatters 0310. All are used in optimizing an independent CTF pointing adesired receiving power density level toward element 2 of the Rx array0736 of the Arx receiver 0732, while steering two nulls to Rx elements 1and 3 of the Rx array 0736 of the Arx receiver 0732 and concurrently twomore nulls to Rx elements 4 and 5 of the Rx array 0726 of the Brxreceiver 0722.

The corresponding beam weight vectors (BWV) are shown on the lower leftcorners of the respective panels, each featuring 5 complex parametersrepresenting the optimized weighting. There are 5 OB radiation patternpairs, which feature total 5 pairs of BWVs corresponding to two sets of5 OB radiation patterns. In each set, anyone beam peak of the 5 OBradiations is always at nulls of all other 4 OB radiations. We only showone of 5 OB radiation pairs.

It is clearly noticed in FIG. 13 that the significant different radiatedpower levels (with respect to a maximum or an averaged power densitylevel over the plotted range) at the intended beam peaks (the desiredbeams at Rx element 2) in the two panels 1302 and 1304). The peak andthe averaged radiation levels in Panel A 1302 feature, respectively, ˜40dB and ˜20 dB above the reference at 0 dB, while those in Panel B 1304are ˜15 dB and ˜5 dB above the 0-dB reference. The observation on thesimulated results suggests that it would require more radiated power forscenarios with LOS effects only than those with both e LOS effects andeffects with scatters. The observed phenomenon appears in all 4 otherpairs.

Rx CTF formulations and optimizations are not shown in this disclosure.

The following simulation results will show, among other phenomena, theeffects of scatters distributions to the optimization capability inCTFs. Tx groups with Intra-networks and Rx groups in S-band may beseparated by up to 100 meters. Current simulations are setup forscenarios under the following conditions;

-   -   (1) all Tx elements are aligned along a line parallel to y-axis        at x=Xt where Xt is at −15 m,    -   (2) all Rx elements along a line parallel to y-axis at x=Xr        where Xr is a constant at 85 m, and    -   (3) all scatters are distributed near a line parallel to y-axis        at x=Xs; where Xs may vary between −1 m to 1 m. They are also        placed in a controllable range of Y near x=Xs. Scatters are        placed with a maximum spacing Y at 10, 20, 40 or 80 m.

FIG. 14 depicts two optimized radiations 1402 and 1404 between Tx and Rxover a 100 m distance; panel (A) 1402 with LOS effects only, and panel(B) 1404 with LOS effects and those from active scatters 0310distributed over a 10 m linear range along y axis. They are both aimingfor designs with 5× frequency re-using.

It is also clearly in FIG. 14 that the significant different radiatedpower levels (with respect to a maximum or an averaged power densitylevel over the plotted range) at the intended beam peaks (the desiredbeam positions at element 1 of the Rx array 0734 of Arx 0732) in the twopanels 1402 and 1404. The peak and averaged radiation levels in Panel A1402 feature, respectively, >45 dB and >30 dB above the reference at 0dB, while those in Panel B 1404 are ˜35 dB and ˜20 dB above thereference. The observations suggest that it would require more radiatedpower for scenarios with LOS effects only than those with effects fromboth LOS and scatters. The observed phenomenon appears in all 4 otherpairs. The optimized BWV are shown accordingly on the left side of thepanels

FIG. 15 depicts 3 calculated patterns for three optimized CTF's 1502,1504 and 1506 under three different scatter distribution conditions. Thethree associated beams feature a fixed radiation level pointing toelement 1 of Arx with the 5 active scatters distributed near linearly iny-direction and near uniformly over various Δy;

-   -   1. panel (A) 1502 with Δy set at 20 m,    -   2. panel (B) 1504 with Δy set at 40 m, and    -   3. panel (C) 1506 with Δy set at 80 m, respectively.

The reference power density level of a receiving element located at theindex 169 is always set at 0 dBm.

All optimization simulation runs are performed under another additionalconstraint of minimum total radiations from both Atx 0710 and Btx 0410.

It is noticed that the average power levels (by eye-balls) over anobservable range along the y-axis are, respectively,

-   -   1. Panel (A) 1502˜10 dBm,    -   2. Panel (B) 1504˜7 dBm, and    -   3. Panel (C) 1506˜4dBm.

They are all aiming for designs with 5× frequency re-use.

FIG. 16 depicts a relationship (including a geometry) of calculating areceived power at a destination, Y, from a power source, X. Conventionallink calculations are used for received power at the destination “Y” viaa line-of-sight (LOS) path in Panel (a) 1602, and its formulation isrepeated in here;

P _(yo) =[P _(x) G _(x)/(4πR _(o) ²)]*Ar_(y)   (2)

where; P_(yo) is received power at location “Y” via a LOS path;

-   -   P_(x) is transmitting power from location “X”;    -   G_(x) is transmitting antenna gain at location “X” in a        direction pointed toward location Y;    -   R_(o) is the LOS distance from location “X” to location “Y”;    -   Ar_(y) is the effective receiving aperture area of a receiving        antenna at location “Y.”

Similarly, in calculation of received power at location “Y” originatedat location “X” and scattered by an active scatter at location “Z” asdepicted in panel (b) 1604 conventional link calculations are usedtwice; a first time for received power at location “Z” from a source atlocation “X” via a line-of-sight (LOS) path, and a second time alsodestination “Y” from the re-radiation via another line-of-sight (LOS)path in panel (b) 1604 and its formulations are repeated in here;

P _(z) =[P _(x) G _(x)/(4πR ₁ ²)]*Ar_(z)   (3a)

where; P_(z) is received power at location “Z” from a source at location“X” via a LOS path;

-   -   P_(x) is transmitting power from location “X”;    -   G_(x) is transmitting antenna gain at location “X” in a        direction pointed toward location Y;    -   R₁ is the LOS distance from location “X” to location “Z”;    -   Ar_(z) is the effective receiving aperture area of a scatter at        location “Z.”

and

P _(y1) =[P _(z1) G _(z)/(4πR ₂ ²)]*Ar_(y)   (3b)

where; P_(y1)is received power at location “Y” from scattering atlocation “Z” via a LOS path;

-   -   P_(z1) is re-radiated power from location “Z”;    -   G_(z) is an equivalent antenna gain at location “Z” in a        direction pointed toward location Y;    -   R₂ is the LOS distance from location “Z” to location “Y”;    -   Ar_(y) is the effective receiving aperture area of a receiving        antenna at location “Y.”

In equation (3a) and (3b), we further assume P_(z1)=P_(z); that receivedpower by an active scatter at “Z” will be re-radiated completelyaccording to its equivalent radiation aperture.

It is also noticed that in general when the scatter is on the directline of XY; or

R ₁ +R ₂ ≥R _(o)   (4)

In 1678, Huygens proposed that every point which a luminous disturbancereaches becomes a source of a spherical wave; the sum of these secondarywaves determines the form of the wave at any subsequent time. He assumedthat the secondary waves travelled only in the “forward” direction andit is not explained in the theory why this is the case. He was able toprovide a qualitative explanation of linear and spherical wavepropagation, and to derive the laws of reflection and refraction usingthis principle, but could not explain the deviations from rectilinearpropagation that occur when light encounters edges, apertures andscreens, commonly known as diffraction effects.

Following Huygens principle, when there are sufficient virtual scattersin form of a cluster in a small volume, effects of their coherentcomponents of re-radiations at the destination “Y” shall be asuperposition from individual effects of all scatters in the cluster.The “effect” from a single scatter is prescribed by equation (3a) and(3b) or simply equation (3). We introduce a term “fetch factor” or Ff ofa selected scatter, to represent the superposition over effects of allvirtual scatters in the cluster or a “volume of coherency” around theselected scatter. When the selected virtual scatter happens to be on thedirect line between location X and location Y as plotted in panel (c)1606, then equation 4 will become

R ₁ +R ₂ =R _(o)   (4a)

The result yielded from equation (2) and that from equation (3) shall beidentical. That formulation on panel (c) 1606 is repeated here as;

P _(yo)=Ff*P _(y1)   (5)

FIG. 16A depicts formulations in calculating a Fetch factor (Ff); powerat a destination via line -of-sights path 1612, and power at destinationvia a virtual scattering mechanism 1614. For a LOS propagation

Po _(ry) =[P _(tx) G _(tx)/(4πR _(o) ²)]*Ar_(y)=(A _(tx) *Ar _(y) /R_(o) ^(2*) ^(λ) ²)   (6)

And for propagation via a virtual scatter,

P _(rz) =[P _(tx) G _(tx)/(4πR ₁ ²)]*Ar_(z),   (7a)

and

P1_(ry) =[P _(tz) G _(tz)/(4πR ₂ ²)]*Ar_(y)   (7b)

Assuming P_(tz)=P_(rz), then

$\begin{matrix}\begin{matrix}{{P\; 1_{ry}} = {\left\lbrack {P_{tz}{G_{tz}/\left( {4\pi \; R_{2}^{2}} \right)}} \right\rbrack*{Ar}_{y}}} \\{= {P_{tx}G_{tx}G_{tz}*{{Ar}_{y}\left\lbrack {\left( {4\pi \; R_{1}^{2}} \right)*\left( {4\pi \; R_{2}^{2}} \right)} \right\rbrack}*{Ar}_{z}}}\end{matrix} & (9)\end{matrix}$

FIG. 16B depicts continued formulations 1616 in calculating a Fetchfactor (Ff) for a virtual scatter so that the resulting power in adestination from a LOS method 1612 shall be identical to that viacalculating scattering effects by a virtual scatter 1614.

Setting P1_(ry)=Po_(ry),

$\begin{matrix}\begin{matrix}{{1/\left( {4\pi \; R_{o}^{2}} \right)} = {{Ff}*G_{tz}*{{Ar}_{z}/\left( {4\pi \; R_{1}^{2}} \right)}\left( {4\pi \; R_{2}^{2}} \right)}} \\{= {{Ff}*A_{tz}*{{Ar}_{z}/\left\lbrack {4\pi \; \lambda^{2}R_{1}^{2}R_{2}^{2}} \right\rbrack}}}\end{matrix} & (9) \\{{therefore};{{Ff} = {\lambda^{2}R_{1}^{2}{R_{2}^{2}/\left( {R_{o}^{2}A_{tz}*{Ar}_{z}} \right)}}}} & (10)\end{matrix}$

Since Ff is a dimensionless factor, it can be re-written as followingafter we further assume G_(rz)=G_(ta)=1, or A_(tz)=Ar_(z)=λ²/4λ, then

Ff=(4π)² R ₁ ² R ₂ ²/(R _(o) ² ^(λ) ²)=[4π*R ₁ *R _(2/)(R_(o)*λ)]²  (11)

or

Ff(dB)=20*log10[4π*R ₁ *R _(2/)(R_(o)*λ)]  (11a)

FIG. 16C depicts calculated distributions of Fetch factor (Ff) in dBnumerically due to propagation effects including locations of scattersand 3 different total propagation distances. The Ff curves are plottedvs ratios of R₁/R_(o) in between 0.01 and 0.99.

It is also noticed that the power density at destination over the LOSpath can be used to gauge importance of path effects other than LOS;especially from an active scatter. When the scattered power density by ascatter arriving the destination were modulating signals at destination,say 20 dB below that of LOS path. There might be many of those low levelscattering. However, an aggregated power level from 10 of them willstill be 1/10^(th) of the power density of the LOS path. The activescattering would have very limited effects on that of the LOS path. Nomatter how we made variations on amplitudes and phases on the low levelscattered power densities.

On the other hand, when the scattered power density by a second set ofscattering platforms arriving the destination, each with 0 dB below thatpower density of LOS path. As a result, aggregated power levels fromthese scattering paths would have very significant effects on that ofthe LOS path. These re-radiated power levels would be able tosignificantly “modulate” signals from the LOS path at destination. TheFf may also be defined as an “amplification factor” or an “amplitudegain” in a repeater (on a scattering platform) so that the re-radiatedpower level from the repeater equal to that of a LOS path at thereceiver in a destination.

When R_(o) at 1000λ, or 120 m at 2.5 GHz, the curve 1622 shows that a Ffof 70 dB is required to become an effective scatter at a location whereR₁/R_(o)=0.5 or ˜60 m away from a source and 60 m away for a destinationin simulations. It also implies an integrated 70 dB gain is need for areal active repeater to become an effective scatter for 120 m wirelesscommunications links.

When R_(o) at 500λ, or 60 m at 2.5 GHz, the curve 1624 shows that a Ffof 65 dB is needed to become an effective scatter at R₁/R_(o)=0.5 or at˜30 m away from a source and also 30 m away for a destination insimulations. It also implies an integrated 65 dB gain is need for a realactive repeater to become an effective scatter for 60 m communicationslinks.

When R_(o) at 100λ, or 12 m at 2.5 GHz, the curve 1626 shows that a Ffof 50 dB is required to become an effective scatter at R₁/R_(o)=0.5 orat ˜6 m away from a source and also 6 m away for a destination insimulations. It also implies an integrated 50 dB gain is need for a realactive repeater to become an effective scatter for 12 m communicationslinks.

It is also noticed that when R₁/R_(o)=0.01 or 0.99, the required Ff isabout ˜30 dB smaller than those at R₁/R_(o)=0.5 for all three cases1622, 624, and 1626. It is more efficient in generating MIMO formultiple frequency reuse by placing active scatters near a source or adestination than placing them around midpoints or centers of propagationchannels between the source and the destination.

What is claimed is:
 1. A communications system comprising: at least onereceiver having a plurality of receiving elements; a transmittercomprising: a plurality of transmitting elements configured to transmitone or more signals to the receiving elements of the at least onereceiver via a plurality of wireless propagation channels; abeam-forming network having input ports and output ports, receivinginput signal streams at the input ports and outputting the one or moresignals as shaped beams based on a set of composited transfer functionsto the transmitting elements; and a channel measurement unit configuredto perform measurements of components of channel status information togenerate a set of point-to-point transfer functions, each of thepoint-to-point transfer functions characterizing at least onepropagation path from one of the transmitting elements to one of thereceiving elements and generate the set of composited transfer functionsby computing linear combinations of the point-to-point transferfunctions, the composited transfer functions being point-to-multipointtransfer functions characterizing propagation paths from the input portsof the beam-forming network to one or more of the receiving elements. 2.The communications system of claim 1, wherein each of the receivingelements is identified by a user element identification index in thepoint-to-point transfer functions and the at least one receiver isidentified by a user identification index.
 3. The communications systemof claim 1 further comprising: at least one active scattering platformlocated within the wireless propagation channels between the transmitterand the at least one receiver, the at least one active scatteringplatform being configured to receive and amplify the transmitted one ormore signals and re-radiate the amplified received one or more signalstoward the at least one receiver, wherein a location of the at least oneactive scattering platform is provided to the channel measurement unit.4. The communications system of claim 3, wherein the channel measurementunit groups all propagation paths from one of the transmitting elementsto one of the receiving elements and generates a correspondingpoint-to-point transfer function.
 5. The communications system of claim3, wherein the at least one active scattering platform is stationary orrelocatable or mobile.
 6. The communications system of claim 3, whereinthe at least one active scattering platform is a repeater comprising afirst transponder and a second transponder functionally cascaded andspatially separated, the first transponder receiving the transmitted oneor more signals at a first frequency slot, amplifying, filtering,frequency translating the received one or more signals before radiatingthe received one or more signals out at a second frequency slot, thesecond transponder receiving the radiated one or more signals at thesecond frequency slot, amplifying, filtering, frequency translating andpower amplifying the received radiated one or more signals beforere-radiating the power-amplified one or more signals out at the firstfrequency slot.
 7. The communications system of claim 3, wherein the atleast one active scattering platform has at least one of the group ofvariable amplification gain, shapeable receiving antenna gain, andshapeable transmitting antenna gain.
 8. The communications system ofclaim 1, wherein the channel measurement unit comprises an optimizationunit to perform optimization for the shaped beams by updating complexweighting parameters of the composited transfer functions.
 9. Thecommunications system of claim 8, wherein the optimization unit performsoptimization for the shaped beams using beam shaping techniques underperformance constraints associated with locations indexed byidentification of the at least one receiver or by identification of eachof the receiving elements.
 10. The communications system of claim 10,wherein the performance constraints comprise performance constraints ona set of orthogonal beams included in the shaped beams.
 11. A method forwireless communications, comprising: providing at least one receiverhaving a plurality of receiving elements; providing a transmitterincluding a plurality of transmitting elements, a beam-forming networkhaving input ports and output ports, and a channel measurement unit;receiving input signal streams at the input ports of the beam-formingnetwork; outputting, from the output ports of the beam-forming network,one or more signals as shaped beams based on a set of compositedtransfer functions to the transmitting elements; performing, via thechannel measurement unit, measurements of components of channel statusinformation to generate a set of point-to-point transfer functions, eachof the point-to-point transfer functions characterizing at least onepropagation path from one of the transmitting elements to one of thereceiving elements; generating, via the channel measurement unit, theset of composited transfer functions by computing linear combinations ofthe point-to-point transfer functions, the composited transfer functionsbeing point-to-multipoint transfer functions characterizing propagationpaths from the input ports of the beam-forming network to one or more ofthe receiving elements; and transmitting, using the transmittingelements, the shaped beams including the one or more signals to thereceiving elements of the at least one receiver via a plurality ofwireless propagation channels.
 12. The method of claim 11, wherein eachof the receiving elements is identified by a user element identificationindex in the point-to-point transfer functions and the at least onereceiver is identified by a user identification index.
 13. The method ofclaim 11 further comprising: providing at least one active scatteringplatform located within the wireless propagation channels between thetransmitter and the at least one receiver; providing a location of theat least one active scattering platform to the channel measurement unit;receiving the transmitted one or more signals, via the at least oneactive scattering platform; amplifying the received one or more signals,via the at least one active scattering platform; and re-radiating theamplified one or more signals toward the at least one receiver, via theat least one active scattering platform.
 14. The method of claim 13,wherein performing measurements of components of channel statusinformation comprises grouping all propagation paths from one of thetransmitting elements to one of the receiving elements and generating acorresponding point-to-point transfer function.
 15. The method of claim13, wherein providing the at least one active scattering platformincludes providing at least one stationary or relocatable or mobileactive scattering platform.
 16. The method of claim 13, whereinproviding the at least one active scattering platform includes providinga repeater comprising a first transponder and a second transponderfunctionally cascaded and spatially separated, the first transponderreceiving the transmitted one or more signals at a first frequency slot,amplifying, filtering, frequency translating the received one or moresignals before radiating the received one or more signals out at asecond frequency slot, the second transponder receiving the radiated oneor more signals at the second frequency slot, amplifying, filtering,frequency translating and power amplifying the received radiated one ormore signals before re-radiating the power-amplified one or more signalsout at the first frequency slot.
 17. The method of claim 11 furthercomprising: performing optimization for the shaped beams, via anoptimization unit included in the channel measurement unit, by updatingcomplex weighting parameters of the composited transfer functions. 18.The method of claim 17, wherein the optimization unit performsoptimization for the shaped beams using beam shaping techniques underperformance constraints associated with locations indexed byidentification of the at least one receiver or by identification of eachof the receiving elements.
 19. A method for wireless communications,comprising: providing a receiver comprising a plurality of receivingelements and a channel measurement unit and having output port;providing at least one transmitter having a plurality of transmittingelements configured to transmit one or more signals to the receivingelements of the receiver via a plurality of wireless propagationchannels; providing at least one active scattering platform locatedwithin the wireless propagation channels between the at least onetransmitter and the receiver, the at least one active scatteringplatform being configured to receive and amplify the transmitted one ormore signals and re-radiate the amplified one or more signals toward thereceiver; performing, via the channel measurement unit, measurements ofcomponents of channel status information to generate a set ofpoint-to-point transfer functions, each of the point-to-point transferfunctions characterizing propagation paths from one of the transmittingelements to one of the receiving elements; and generating, via thechannel measurement unit, a set of composited transfer functions bycomputing linear combinations of the point-to-point transfer functions,the composited transfer functions being multipoint-to-point transferfunctions characterizing propagation paths from one or more of thetransmitting elements to the output port of the receiver andrepresenting shaped receiving beams for the receiving elements toreceive the re-radiated one or more signals.
 20. The method of claim 19further comprising: performing optimization of the shaped receivingbeams, via an optimization unit included in the channel measurementunit, by updating complex weighting parameters of the compositedtransfer functions.